Time-dependent heat transfer coefficient of a wall

2003 ◽  
Vol 27 (9) ◽  
pp. 795-811 ◽  
Author(s):  
Periklis E. Ergatis ◽  
Panagiotis G. Massouros ◽  
Georgia C. Athanasouli ◽  
George P. Massouros
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Time Dependent

Heat Transfer Coefficient in Rapid Solidification of a Liquid Layer on a Substrate

2000 ◽  
Vol 122 (4) ◽  
pp. 792-800 ◽  
Author(s):  
P. S. Wei ◽  
F. B. Yeh
Keyword(s):  
Heat Transfer ◽  
Heat Transfer Coefficient ◽  
Transfer Coefficient ◽  
Biot Number ◽  
Equilibrium Phase ◽  
Density Ratio ◽  
Solid Substrate ◽  
Time Dependent ◽  
Bottom Surface ◽  
Melting Front

The heat transfer coefficient at the bottom surface of a splat rapidly solidified on a cold substrate is self-consistently and quantitatively investigated. Provided that the boundary condition at the bottom surface of the splat is specified by introducing the obtained heat transfer coefficient, solutions of the splat can be conveniently obtained without solving the substrate. In this work, the solidification front in the splat is governed by nonequilibrium kinetics while the melting front in the substrate undergoes equilibrium phase change. By solving one-dimensional unsteady heat conduction equations and accounting for distinct properties between phases and splat and substrate, the results show that the time-dependent heat transfer coefficient or Biot number can be divided into five regimes: liquid splat-solid substrate, liquid splat-liquid substrate, nucleation of splat, solid splat-solid substrate, and solid splat-liquid substrate. The Biot number at the bottom surface of the splat during liquid splat cooling increases and nucleation time decreases with increasing contact Biot number, density ratio, and solid conductivity of the substrate, and decreasing specific heat ratio. Decreases in melting temperature and liquid conductivity of the substrate and increase in latent heat ratio further decrease the Biot number at the bottom surface of the splat after the substrate becomes molten. Time-dependent Biot number at the bottom surface of the splat is obtained from a scale analysis. [S0022-1481(00)01004-5]

scholarly journals Analytical Solution of Heat Conduction for Hollow Cylinders with Time-Dependent Boundary Condition and Time-Dependent Heat Transfer Coefficient

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Te-Wen Tu ◽  
Sen-Yung Lee
Keyword(s):  
Heat Transfer ◽  
Boundary Condition ◽  
Heat Transfer Coefficient ◽  
Analytical Solution ◽  
Transfer Coefficient ◽  
Time Dependent ◽  
Physical Parameters ◽  
Expansion Theorem ◽  
Present Solution ◽  
Hollow Cylinders

An analytical solution for the heat transfer in hollow cylinders with time-dependent boundary condition and time-dependent heat transfer coefficient at different surfaces is developed for the first time. The methodology is an extension of the shifting function method. By dividing the Biot function into a constant plus a function and introducing two specially chosen shifting functions, the system is transformed into a partial differential equation with homogenous boundary conditions only. The transformed system is thus solved by series expansion theorem. Limiting cases of the solution are studied and numerical results are compared with those in the literature. The convergence rate of the present solution is fast and the analytical solution is simple and accurate. Also, the influence of physical parameters on the temperature distribution of a hollow cylinder along the radial direction is investigated.

Application of the Time-Dependent Overall Heat-Transfer Coefficient Concept to Heat-Transfer Problems in Porous Media

1984 ◽  
Vol 24 (01) ◽  
pp. 107-112 ◽  
Author(s):  
Abdurrahman Satman ◽  
Anatoly B. Zolotukhin ◽  
Mohamed Y. Soliman
Keyword(s):  
Heat Transfer ◽  
Porous Media ◽  
Heat Transfer Coefficient ◽  
Energy Balance ◽  
Transfer Coefficient ◽  
Heat Loss ◽  
Thermal Recovery ◽  
Time Dependent ◽  
Overall Heat Transfer Coefficient ◽  
Recovery Processes

Abstract Prediction of temperature distribution behavior during thermal recovery processes is necessary for engineering, evaluation of field operations. Such a prediction can be used in the case of hot- and cold-water injection into a reservoir and also applies in some other thermal recovery processes, such as in-situ combustion and steam-flooding. The mathematical formulas discussed involve the concept of a time-dependent overall heat-transfer coefficient. In the first portion of the paper, we discuss two new analytical solutions that describe the temperature distribution in linear and radial reservoirs in the case of hot- and cold-water injection. A comparison with published laboratory hot-water injection data demonstrates the validity of the solution for linear geometry. Since the new analytical model considers the heat conduction in addition to convection and heat loss. It describes the thermal behavior in a more general form than does Lauwerier's model. These two models are compared also. The application of the time-dependent overall heat-transfer coefficient concept to the thermal behavior of the steam plateau portion of the in-situ combustion process is discussed in the second pail of the paper. The result is fairly satisfactory. Introduction Since the mid-1950's, many models describing the temperature behavior and thermal efficiency of fluid injection into porous media have been formulated and solved analytically. In particular, increasing demands for thermal oil recovery processes and heat extraction processes from geothermal fields have led researchers to develop these models. With advancements in numerical solution techniques, it also has become possible to obtain solutions to problems that could not have been solved before. Heat-transfer models in porous media consider three heat-transfer mechanisms: thermal conduction, convective transfer between fluid and solid matrix, and energy transfer resulting from fluid flow. The conductive heat transfer describes the thermal conduction in the direction of flow. Convective heat transfer is accounted for by the assumption of thermal equilibrium between the porous medium and its contained fluids. The heat loss caused by fluid injection plays an important role. Keeping the loss low is a primary concern for the efficiency of thermal recovery processes. Although the heat is transferred by a combination of both conduction and convection, in earlier formulations of the energy balance of flow in porous media, the heat loss generally has been treated as either a convective or conductive heat-transfer mechanism. A constant overall heat-transfer coefficient, U, can be used to describe the heat transfer from the system to the adjacent strata: q = UA (T-Ti)........................................(1) This has proved a reasonable approximation for the heat-loss mechanisms occurring in nonadiabatic laboratory tube experiments. Eq. 1 describes the heat loss in a convective form. Heat loss in conductive form can be written as Tq=k A ---- ........................................(2)adj y However, such formulation of heat loss leads to a two-dimensional energy balance equation for one-dimensional flow geometry or a three-dimensional energy balance equation for two-dimensional flow geometry. The solutions of such energy-balance equations become difficult. Lauwerier used the conductive form of heat loss in his model and developed an analytical solution for temperature propagation in a linear flow geometry. He assumed all infinite thermal conductivity in the vertical direction within permeable sand. The reservoir and surrounding formation thermal conductivities in the horizontal direction, however, were neglected. Later, in 1959, Rubinshtein developed it more sophisticated analytical model for heat flow in porous media. His model removed the restrictions in dealing with the thermal conductivities in Lauwerier's model. SPEJ P. 107^

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